A coworker brought in this problem his daughter had been given in her eighth grade math class. The challenge is to find the next three elements, and we’re all baffled. Personally, I think someone has screwed up the numbers. If the SDMB can’t get it, I’ll know I’m right.
2,32,2,64,2,128 no idea…
1,4,2,8,2,16,3,32,3,64,3,128,4,256,4,…?
Yeah, that’s the best I came up with too. If it were 2,4,2,8,2,16… then that would make sense, but starting with 1? I don’t think so.
I’m not following that. Can you explain your reasoning?
1,4,2,8,2,16,4,32,4,64,8,128
or
one-fourth,one-fourth, one-eighth, one-eighth, one-sixteenth, one-sixteenth, and so on
There is one 1, two 2s, three 3s etc. - shuffled into the powers of 2
It would logically consistent, but not correct in any mathematical sense
This is what i came up with, but i think it’s a stupid question. And it’s not really a math question at all.
It’s not cataloged as a well known integer series: 1,4,2,8,2,16 - OEIS
Assuming the series is limited to powers of 2, a equivalent series would be the exponents:
0, 2, 1, 3, 1, 4, …
What’s the rule there?
That makes sense to me. I just wasn’t getting the 1 and 2’s, but that solution works.
A valid answer that the teacher will probably call wrong is 1,4,2,8,2,16 again. So the next three elements would be 1,4,2.
But I like Sahirnee’s answer.
There is 1 1, 2 2s, 3 3s, and so on
Sometimes in number patterns the pattern skips over numbers
so that every other number follows a pattern, or every third number follows a pattern.
so this pattern could be
1,4,2,8,2,16,3,32,3,64,3,128,4
I don’t think it’s obvious what the next item in the series
1, 2, 2, …
is. The series could be:
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 5, …
(That’s the number of factors, including itself and 1, of each of the natural numbers: 1 factor of 1, 2 factors of both 2 and 3, 3 factors of 4, etc.)
That’s a problem with number sequences, quite often there are more than one correct answer.
Everybody’s brain works differently and what jumps out at one person isn’t apparent to another.
I don’t know that my answer is right but it’s the direction my brain took.
Your answer is right, it just may not be the one right answer the author of the sequence is looking for.
The current sequence, from bit shifting perspective is:
<< 2
>> 1
<< 2
>> 2
<< 3
So one possible continuation would be:
>> 3
<< 3
>> 4
That would make the full pattern:
1,4,2,8,2,16,2,16,1
Why can’t this be the pattern?
1,4,2,8,2,16,1,32,2,64,2,128,1,256…
My arbitrary (yet correct) answer:
f(1) = 1
f(2) = 4
If x is odd, f(x) = f(x-2) / ( 2*f(x-1) )
If x is even, f(x) = f(x-2) * f(x-1)
Therefore:
f(3) = 2
f(4) = 8
f(5) = 2
f(6) = 16
f(7) = 4
f(8) = 64
f(9) = 8
f(10) = 512
f(11) = 32
f(12) = 16384
f(13) = 256
f(14) = 4194304
etc.
If forced to guess, though, I would expect a typo and the actual question would be 1, 4, 2, 8, 3, 16.
The problem with number sequence problems is how damned smug the person who creates the question is. Thinks s/he’s so great. Let me tell you something, number sequence maker-upper: you’re not great at all. You suck.
You’re right, it isn’t obvious - it could equally be 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2… - a sequence that will probably be familiar to anyone who has played in an orchestra, especially brass or percussion!
Ha! I agree that the most likely answer in this case is a typo. The student’s best bet might be to give one (or more) of the answers in this thread and add the possibility of the typo, for which a nice teacher might give extra credit. A nasty teacher might mark it as wrong and just give the arbitrary answer the question-setter has decided on.